A variety of system identification methods are available for linear time invariant (LTI) systems. For example, in non-parametric frequency-domain estimation methods, the system is subjected to a white noise input, the output is represented in the frequency domain, and the user fits a model that is determined by the number of resonance frequencies and the decay rate of the power spectrum. On the other hand, parametric methods presuppose a system representation, such as an auto regressive moving average (ARMA) model or a state space (SS) model, where the order of the system is estimated first using auto correlation, and the system identification problem is reduced to a parameter estimation problem, solved using numerical gradient descent methods to minimize a suitable error metric (c.f.[1]}).
